Hiroki Sayama sayama@binghamton.edu NECSI Summer School 2008 Week 2: Complex Systems Modeling and Networks Fundamentals of Modeling Hiroki Sayama sayama@binghamton.edu

Introduction

Examples of complex systems Chemical networks Gene networks Organisms Physiologies Brains Ecosystems Economies Societies Internet

Several characteristics of complex systems Networks of many components Nonlinear interactions Self-organization Structure/behavior that is neither regular nor random Emergent behavior

Topics to be covered Fundamentals of Modeling Non-Spatial Models Cellular Automata Agent-Based Models Network Models

Course format Each module (~3 hrs.) includes Basic concepts of model framework Walkthrough of sample codes Coding exercises Application and discussion Free Q&As and discussion at the end of each day

Course emphasis Emphasis will be on the process of model development itself Examples are no more than to show how to implement various models Feel free to share your thought with class whenever you come up with interesting modeling ideas The whole class will work together to develop and/or evaluate your model

Online resource All the course slides and sample codes are (or will be) available at: http://coco.binghamton.edu/NECSI/ Login name: necsi Password: com3sysB

Models in Science and Engineering

Science finds these kinds of laws (and engineering uses them) F = m a F = G m1 m2 / r2 P V = n R T V = I R E = m c2 Conservation of energy, momentum and angular momentum etc…

Cycle of scientific efforts Observe Nature Develop a hypothesis that explains the observations Make some predictions using your hypothesis Carry out experiments to see if the predictions are correct If correct, your hypothesis is proven If not, you have to develop another hypothesis ?

Let’s do some logic A phenomenon P is observed You come up with hypothesis H that explains P (i.e., H  P) You predict another phenomenon Q using hypothesis H (i.e., H  Q) You conduct experiments to see Q What if “Q” is actually observed? What if “not Q” is observed?

Easy to disprove, hard to prove If “not Q” is observed, H is easily disproved (H  Q)  (not Q  not H) (contraposition) If “Q” is observed, we are not yet sure whether H is by itself right or not Maybe H would need additional condition K we were not aware in experiments to cause Q (limitation of applicability) Maybe another hypothesis R could also explain P and Q (possibility of alternative hypothesis)

Fallacy of “scientific truth” People often say “This is scientifically proven”, but strictly speaking -- there is NO way to scientifically “prove” anything about real Nature All laws are at best “well-tested hypotheses” valid within limited conditions Room for other possible explanations always remain No guarantee for their universal, permanent truth

So, they are all “models”!! F = m a F = G m1 m2 / r2 P V = n R T V = I R E = m c2 Conservation of energy, momentum and angular momentum etc… Valid only in Newtonian mechanics Applicable to ideal cases only Seems to be valid always, but there may be some other ways to explain our universe…

“Model” A simplified representation of a system (either conceptual, verbal, diagrammatic, physical or formal) You are always creating a model in your mind when you try to understand the external world Worldviews, religions, cultures Natural/social sciences

Models in science Science is an endless effort to create “models” of Nature What you’ve learned as “scientific truth” are actually the collection of “models” that have survived many attempts to disprove them so far Modeling is the one and only rational approach to the unreachable reality

Models in engineering Engineering is to control Nature to make something happen in it The real Nature is unreachable though  What we can actually control are “models” of Nature Models are a logical construction; you can have a full control over them Engineering is an endless effort to control Nature by creating and controlling its models

Think about… A couple of models you have learned that are extensively used in today’s scientific/engineering fields How were they developed? What made them more useful than earlier models? How could they possibly be wrong?

How to Create a Model?

Two ways of modeling Descriptive modeling Rule-based modeling Tries to specify the system’s actual (or past) states Images, miniatures, biographies Rule-based modeling Tries to extrapolate the system’s possible (or future) states Theories, principles, equations © Toyo Precision Parts Co., Ltd. © Gramercy

Keep in mind: Models should be Simple Occam’s razor: Makes short descriptions Correct Produces predictions in good agreement with reality Robust Produces strong conclusions that can hold with various assumptions; broadens applicability

Cycle of modeling efforts Observe the system of interest Reflect on possible rules that might cause the system’s characteristics Derive predictions from those rules and compare them with the reality Repeat the above to modify the rules until you get satisfied (This is exactly what scientists have been doing)

Problems in modeling Observe the system of interest Reflect on possible rules that might cause the system’s characteristics Derive predictions from those rules and compare them with the reality Repeat the above to modify the rules until you get satisfied This is so deeply interwoven with our everyday cognitive processes Heavily depends on one’s past experience and knowledge Hard to teach or learn…

Exercise Create a mathematical model of the following behavior: Some quantity Time

Exercise Create a mathematical model of the following behavior: Some quantity Time

Exercise Create a mathematical model of the following behavior: Some quantity Time

Exercise Create a mathematical model of the following behavior: Some quantity Time

Creating a model of complex systems Define the key questions and choose the right scale of modeling Identify structure (parts and their connections) of the system Define possible states for each part Describe how the state of each part changes over time through interactions with other parts

Exercise Create a conceptual model for each of the following systems by describing which scale you look at, what are their parts, what states they can take, how the parts are connected, and how the states change through interactions between parts

Epistemological challenges in modeling complex systems Many degrees of freedom Parallelism Non-linearity Sensitivity to initial conditions Pattern formation Difficult to handle with traditional “reductionism” approaches

Epistemological challenges in modeling complex systems Behavior of complex systems often contradict our everyday experiences It is very hard to come up with underlying microscale rules that could explain those macroscale outcomes One needs to get “experienced” and “familiar” with them to develop a better model of complex systems

Computer simulation Reconstruct your model in full detail in a computer, and let it actually show (rather than predict) its behavior Powerful tool for studying large, discrete, and/or inhomogeneous systems, through interactive and intuitive “experiences” of various possible model dynamics Virtually no better tools available for general complex systems studies

Various tools for simulation General programming languages C, C++, Java, Python, etc. Free simulation software packages StarLogo, NetLogo, Swarm, etc. Commercially available applications MATLAB, Mathematica, MS Excel, etc.

How to Evaluate a Model?

Simplicity Is your model simple enough? Are you getting more “outputs” from the model than “inputs” you gave to the model? Can’t you reduce some of the parameters/variables from the model?

Correctness Does your model produce “correct” results? Accurate predictions may not be practical for complex systems behaviors Correctness may be “conceptual” or “quantitative” Is the simulation free from mistakes? Do different implementations produce the same results?

Robustness Are the results similar even if you slightly change: Initial conditions Parameter values Model assumptions To confirm the robustness, conduct: Systematic experiments testing the variations listed above Independent model development and their comparison within group

However… There is no single scale for evaluating the values of models Similar to worldviews, religions, etc. Ultimately, models are evaluated socially E.g. # of users, papers You should advocate your model if you believe it is better than others